Log24

Saturday, September 24, 2016

The Seven Seals

Filed under: General,Geometry — Tags: — m759 @ 7:23 AM

From Hermann Weyl's 1952 classic Symmetry —

"Galois' ideas, which for several decades remained
a book with seven seals  but later exerted a more
and more profound influence upon the whole
development of mathematics, are contained in
a farewell letter written to a friend on the eve of
his death, which he met in a silly duel at the age of
twenty-one. This letter, if judged by the novelty and
profundity of ideas it contains, is perhaps the most
substantial piece of writing in the whole literature
of mankind."

Some Galois geometry —

See the previous post for more narrative.

Sunday, June 5, 2016

Sunday School: Seven Seals

Filed under: General,Geometry — m759 @ 7:00 AM

A set of 7 partitions of the 2x2x2 cube that is invariant under PSL(2, 7) acting on the 'knight' coordinatization

Click image for some background.

See also Standard Disclaimer.

Monday, April 25, 2016

Seven Seals

Filed under: General,Geometry — Tags: — m759 @ 11:00 PM

 An old version of the Wikipedia article "Group theory"
(pictured in the previous post) —

"More poetically "

From Hermann Weyl's 1952 classic Symmetry

"Galois' ideas, which for several decades remained
a book with seven seals  but later exerted a more
and more profound influence upon the whole
development of mathematics, are contained in
a farewell letter written to a friend on the eve of
his death, which he met in a silly duel at the age of
twenty-one. This letter, if judged by the novelty and
profundity of ideas it contains, is perhaps the most
substantial piece of writing in the whole literature
of mankind."

The seven seals from the previous post, with some context —

These models of projective points are drawn from the underlying
structure described (in the 4×4 case) as part of the proof of the
Cullinane diamond theorem .

Sunday, January 7, 2018

Space Program

Filed under: General,Geometry — Tags: — m759 @ 12:00 AM

Or:  Interality Illustrated

See also Seven Seals.

Tuesday, April 26, 2016

Interacting

Filed under: General,Geometry — m759 @ 8:31 PM

"… I would drop the keystone into my arch …."

— Charles Sanders Peirce, "On Phenomenology"

" 'But which is the stone that supports the bridge?' Kublai Khan asks."

— Italo Calvino, Invisible Cities, as quoted by B. Elan Dresher.

(B. Elan Dresher. Nordlyd  41.2 (2014): 165-181,
special issue on Features edited by Martin Krämer,
Sandra Ronai and Peter Svenonius. University of Tromsø –
The Arctic University of Norway.
http://septentrio.uit.no/index.php/nordlyd)

Peter Svenonius and Martin Krämer, introduction to the
Nordlyd  double issue on Features —

"Interacting with these questions about the 'geometric' 
relations among features is the algebraic structure
of the features."

For another such interaction, see the previous post.

This  post may be viewed as a commentary on a remark in Wikipedia

"All of these ideas speak to the crux of Plato's Problem…."

See also The Diamond Theorem at Tromsø and Mere Geometry.

Saturday, June 11, 2016

Where Credit Is Due

Filed under: General — Tags: — m759 @ 4:16 AM

"White is credited with broadening the scope of
topics traditionally studied by philosophers…."

Monday, June 6, 2016

Structure and Sense

Filed under: General,Geometry — Tags: — m759 @ 2:01 PM

"… the war of 70-some years ago
has already become something like the Trojan War
had been for the Homeric bards:
a major event in the mythic past
that gives structure and sense to our present reality."

— Justin E. H. Smith, a professor of philosophy at
     the University of Paris 7–Denis Diderot,
     in the New York Times  column "The Stone"
     (print edition published Sunday, June 5, 2016)

In memory of a British playwright who reportedly
died at 90 this morning —

Structure

Sense

A set of 7 partitions of the 2x2x2 cube that is invariant under PSL(2, 7) acting on the 'knight' coordinatization

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